Linearity and non-linearity in cerebral hemodynamics

Background: Transcranial Doppler ultrasound has been extensively used to study cerebral hemodynamics, and yet the basic characteristics of the input/output system of blood pressure/velocity are little known. We examine whether this system can best be considered linear or non-linear. Methods: We assessed the adequacy of linear modeling in four ways: (1) Known properties of cerebral blood flow were reviewed and analyzed from a systems standpoint; (2) 1100 ARX & OE model types were tested with data from 29 normal subjects, with and without lowpass filtering; (3) time-frequency analysis was used to identify nonstationary behavior and markers of non-linearity (such as bifurcations, chirps, and intermittent autoregulatory impairment) in the same data sets; (4) simple computer models of autoregulation incorporating time delays and non-linear elements were tested for production of spontaneous oscillations. Results: (1) Several aspects of cerebral hemodynamics are poorly described by linear models, (2) the ARX & OE models performed poorly, (3) time-frequency analysis showed non-linear and nonstationary behavior, (4) the computer models produced spontaneous oscillations similar to those observed in humans. Conclusions: There is strong evidence that the blood pressure/velocity system is non-linear.